Find the longest sub-string which is prefix, suffix and also present inside the string

Given a string str. The task is to find the longest sub-string which is a prefix, a suffix and a sub-string of the given string, str. If no such string exists then print -1.

Examples:

Input: str = “fixprefixsuffix”
Output: fix
“fix” is a prefix, suffix and present inside in the string too.

Input: str = “aaaa”
“aa” is a prefix, suffix and present inside the string.

Approach: Let us calculate the longest prefix suffix for all prefixes of string. longest prefix suffix lps[i] is maximal length of prefix that also is suffix of substring [0…i]. More about longest prefix suffix you can see in a description of kmp algorithm.



The first of possible answers is a prefix of length lps[n-1]. If lps[n-1] = 0, there is no solution. For checking the first possible answer you should iterate over lps[i]. If at least one of them equal to lps[n-1] (but not n-1th, of course) – you found the answer. The second possible answer is a prefix of length lps[lps[n-1]-1]. If lps[lps[n-1]-1] = 0, you also have no solution. Otherwise, you can be sure that the answer already found. This substring is a prefix and a suffix of our string. Also, it is a suffix of a prefix with length lps[n-1] that places inside of all string. This solution works in O(n).

Below is the implementation of the above approach:

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to find longest prefix suffix
vector<int> compute_lps(string s)
{
    int n = s.size();
  
    // To store longest prefix suffix
    vector<int> lps(n);
  
    // Length of the previous
    // longest prefix suffix
    int len = 0;
  
    // lps[0] is always 0
    lps[0] = 0;
    int i = 1;
  
    // Loop calculates lps[i] for i = 1 to n - 1
    while (i < n) {
        if (s[i] == s[len]) {
            len++;
            lps[i] = len;
            i++;
        }
  
        // (pat[i] != pat[len])
        else {
            if (len != 0)
                len = lps[len - 1];
            // Also, note that we do not increment
            // i here
  
            // If len = 0
            else {
                lps[i] = 0;
                i++;
            }
        }
    }
  
    return lps;
}
  
// Function to find the longest substring
// which is prefix as well as a
// sub-string of s[1...n-2]
void Longestsubstring(string s)
{
    // Find longest prefix suffix
    vector<int> lps = compute_lps(s);
    int n = s.size();
  
    // If lps of n-1 is zero
    if (lps[n - 1] == 0) {
        cout << -1;
        return;
    }
  
    for (int i = 0; i < n - 1; i++) {
  
        // At any position lps[i] equals to lps[n - 1]
        if (lps[i] == lps[n - 1]) {
            cout << s.substr(0, lps[i]);
            return;
        }
    }
  
    // If answer is not possible
    if (lps[lps[n - 1] - 1] == 0)
        cout << -1;
    else
        cout << s.substr(0, lps[lps[n - 1] - 1]);
}
  
// Driver code
int main()
{
    string s = "fixprefixsuffix";
  
    // function call
    Longestsubstring(s);
  
    return 0;
}
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// Java implementation of the approach
class GFG
{
    // Function to find longest prefix suffix
    static int [] compute_lps(String s)
    {
        int n = s.length();
      
        // To store longest prefix suffix
        int [] lps = new int [n];
      
        // Length of the previous
        // longest prefix suffix
        int len = 0;
      
        // lps[0] is always 0
        lps[0] = 0;
        int i = 1;
      
        // Loop calculates lps[i] for i = 1 to n - 1
        while (i < n) 
        {
            if (s.charAt(i) == s.charAt(len)) 
            {
                len++;
                lps[i] = len;
                i++;
            }
      
            // (pat[i] != pat[len])
            else 
            {
                if (len != 0)
                    len = lps[len - 1];
                // Also, note that we do not increment
                // i here
      
                // If len = 0
                else
                {
                    lps[i] = 0;
                    i++;
                }
            }
        }
      
        return lps;
    }
      
    // Function to find the longest substring
    // which is prefix as well as a
    // sub-string of s[1...n-2]
    static void Longestsubstring(String s)
    {
        // Find longest prefix suffix
        int [] lps = compute_lps(s);
        int n = s.length();
      
        // If lps of n-1 is zero
        if (lps[n - 1] == 0)
        {
            System.out.println(-1);
            return;
        }
      
        for (int i = 0; i < n - 1; i++) 
        {
      
            // At any position lps[i] equals to lps[n - 1]
            if (lps[i] == lps[n - 1]) 
            {
                System.out.println(s.substring(0, lps[i]));
                return;
            }
        }
      
        // If answer is not possible
        if (lps[lps[n - 1] - 1] == 0)
            System.out.println(-1);
        else
            System.out.println(s.substring(0, lps[lps[n - 1] - 1]));
    }
      
    // Driver code
    public static void main (String [] args)
    {
        String s = "fixprefixsuffix";
      
        // function call
        Longestsubstring(s);
      
    }
}
  
// This code is contributed by ihritik 
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# Python3 implementation of the approach
  
# Function to find longest prefix suffix
def compute_lps(s):
  
    n = len(s)
  
    # To store longest prefix suffix
    lps = [0 for i in range(n)]
  
    # Length of the previous
    # longest prefix suffix
    Len = 0
  
    # lps[0] is always 0
    lps[0] = 0
    i = 1
  
    # Loop calculates lps[i] for i = 1 to n - 1
    while (i < n):
        if (s[i] == s[Len]):
            Len += 1
            lps[i] = Len
            i += 1
  
        # (pat[i] != pat[Len])
        else:
            if (Len != 0):
                Len = lps[Len - 1]
            # Also, note that we do not increment
            # i here
  
            # If Len = 0
            else:
                lps[i] = 0
                i += 1
              
  
    return lps
  
# Function to find the longest substring
# which is prefix as well as a
# sub-of s[1...n-2]
def Longestsubstring(s):
  
    # Find longest prefix suffix
    lps = compute_lps(s)
    n = len(s)
  
    # If lps of n-1 is zero
    if (lps[n - 1] == 0):
        print(-1)
        exit()
      
    for i in range(0,n - 1):
  
        # At any position lps[i] equals to lps[n - 1]
        if (lps[i] == lps[n - 1]):
            print(s[0:lps[i]])
            exit()
  
    # If answer is not possible
    if (lps[lps[n - 1] - 1] == 0):
        print(-1)
    else:
        print(s[0:lps[lps[n - 1] - 1]])
  
# Driver code
  
s = "fixprefixsuffix"
  
# function call
Longestsubstring(s)
  
# This code is contributed by mohit kumar
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// C# implementation of the approach
using System;
  
class GFG
{
    // Function to find longest prefix suffix
    static int [] compute_lps(string s)
    {
        int n = s.Length;
      
        // To store longest prefix suffix
        int [] lps = new int [n];
      
        // Length of the previous
        // longest prefix suffix
        int len = 0;
      
        // lps[0] is always 0
        lps[0] = 0;
        int i = 1;
      
        // Loop calculates lps[i] for i = 1 to n - 1
        while (i < n) 
        {
            if (s[i] == s[len])
            {
                len++;
                lps[i] = len;
                i++;
            }
      
            // (pat[i] != pat[len])
            else 
            {
                if (len != 0)
                    len = lps[len - 1];
                // Also, note that we do not increment
                // i here
      
                // If len = 0
                else 
                {
                    lps[i] = 0;
                    i++;
                }
            }
        }
      
        return lps;
    }
      
    // Function to find the longest substring
    // which is prefix as well as a
    // sub-string of s[1...n-2]
    static void Longestsubstring(string s)
    {
        // Find longest prefix suffix
        int [] lps = compute_lps(s);
        int n = s.Length;
      
        // If lps of n-1 is zero
        if (lps[n - 1] == 0) 
        {
            Console.WriteLine(-1);
            return;
        }
      
        for (int i = 0; i < n - 1; i++)
        {
      
            // At any position lps[i] equals to lps[n - 1]
            if (lps[i] == lps[n - 1]) 
            {
                Console.WriteLine(s.Substring(0, lps[i]));
                return;
            }
        }
      
        // If answer is not possible
        if (lps[lps[n - 1] - 1] == 0)
            Console.WriteLine(-1);
        else
            Console.WriteLine(s.Substring(0, lps[lps[n - 1] - 1]));
    }
      
    // Driver code
    public static void Main ()
    {
        string s = "fixprefixsuffix";
      
        // function call
        Longestsubstring(s);
      
    }
}
  
// This code is contributed by ihritik
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<?php
// Python3 implementation of the approach 
  
// Function to find longest prefix suffix 
function compute_lps($s
    $n = strlen($s); 
  
    // To store longest prefix suffix 
    $lps = array(); 
  
    // Length of the previous 
    // longest prefix suffix 
    $len = 0; 
  
    // lps[0] is always 0 
    $lps[0] = 0; 
    $i = 1; 
  
    // Loop calculates lps[i] for i = 1 to n - 1 
    while ($i < $n
    
        if ($s[$i] == $s[$len]) 
        
            $len++; 
            $lps[$i] = $len
            $i++; 
        
  
        // (pat[i] != pat[len]) 
        else 
        
            if ($len != 0) 
                $len = $lps[$len - 1]; 
                  
            // Also, note that we do not increment 
            // i here 
  
            // If len = 0 
            else 
            
                $lps[$i] = 0; 
                $i++; 
            
        
    
  
    return $lps
  
// Function to find the longest substring 
// which is prefix as well as a 
// sub-string of s[1...n-2] 
function Longestsubstring($s
    // Find longest prefix suffix 
    $lps = compute_lps($s); 
    $n = strlen($s); 
  
    // If lps of n-1 is zero 
    if ($lps[$n - 1] == 0)
    
        echo -1; 
        return
    
  
    for ($i = 0; $i < $n - 1; $i++) 
    
  
        // At any position lps[i] equals to lps[n - 1] 
        if ($lps[$i] == $lps[$n - 1])
        
            echo substr($s, 0, $lps[$i]); 
            return
        
    
  
    // If answer is not possible 
    if ($lps[$lps[$n - 1] - 1] == 0) 
        echo -1; 
    else
        echo substr($s, 0, $lps[$lps[$n - 1] - 1]); 
  
// Driver code 
$s = "fixprefixsuffix"
  
// function call 
Longestsubstring($s); 
  
// This code is contributed by Ryuga
?>
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Output:
fix

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